Consistent and accurate methods for performing state estimation in a wide-variety of systems are critical to the function of many processes and operations, both civilian and military. Systems and methods have been developed for state estimation of a system that may transition between different regimes of operation which may be described or defined by a plurality of discrete models. These state estimation methods can be applied to various systems having sensory inputs, by way of non-limiting example only, nuclear, chemical, or manufacturing factories or facilities, control processes subject to external parameter changes, space stations subject to vibrations, automobiles subject to road conditions, and the like. One particularly useful application for state estimation is tracking objects in flight, such as a multistage rocket that is transitioning back and forth between a ballistic model of flight and thrust modes, or an aircraft performing maneuvers mid-flight.
Popular state estimate systems include Kalman filters with white plant noise that are used as reduced state estimators. Recently, Optimal Reduced State Estimation (ORSE) filters for tracking an object have been developed. ORSE filters are reduced state because parametric acceleration is not represented in the filter model but is instead estimated as an independently calculated part of the covariance matrix. The filter is optimal because it reduces errors in the least squares sense. ORSE filters include bounds or maximum excursions for various parameters, and minimizes the mean-square and, thus, the root-mean-square (RMS) estimation errors for the maximum excursions of the parameters in the truth model. Furthermore, because the bounds are included in the minimized covariance, embodiments of the present invention do not need white plant noise, as is required by Kalman filters, to cope with the reduced state. U.S. Pat. No. 7,180,443, issued Feb. 20, 2007 in the names of Mookerjee and Reifler, which is incorporated by reference in its entirety, describes an ORSE state estimator for determining state estimation and state error covariances for generalized or arbitrary motion of a target or moving object where the sensors provide complete measurements, namely each measurement locating a point in three dimensional space at a known time with a non-singular measurement covariance matrix.
Because state estimate systems are critical to the function of many processes and operations, it is important that the covariance fidelity of such systems be assessed. Current tests for the covariance fidelity of state estimate systems are directed to assessing the fidelity of state estimate systems that are based on systems that use Kalman filters with white plant noise. These fidelity tests are inadequate for assessing the fidelity of ORSE systems. The current covariance fidelity test has two major shortcomings: first, there is no standard reference for the ORSE. The cumulative distribution function (cdf) of a multi-variate Gaussian is described by a chi-square distribution with r degrees of freedom, but ORSE bias distribution is specified only by a magnitude limit. Second, the outcome of a standard covariance test on a ORSE is ambiguous, in that further evaluation is required to determine if deviation is associated with the random or the bias component. In addition, for various reasons it is problematic to evaluate multiple independent bias sources represented by a Mahalanobis Distance Value (MDV). Examples are containment less than 100% when bias distribution is unspecified, and 100% containment bounds forming a rectangular prism rather than an ellipsoid.
Systems and methods for assessing the covariance fidelity of ORSE state estimation systems are desired.